Problem: $A$ $B$ $C$ If: $ AB = 2x + 4$, $ AC = 42$, and $ BC = 3x + 8$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {2x + 4} + {3x + 8} = {42}$ Combine like terms: $ 5x + 12 = {42}$ Subtract $12$ from both sides: $ 5x = 30$ Divide both sides by $5$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $BC$ $ BC = 3({6}) + 8$ Simplify: $ {BC = 18 + 8}$ Simplify to find ${BC}$ : $ {BC = 26}$